Point-like or linear marks are made in the surface of a workpiece of metal, wood or plastic by means of a center punch of hard metal. Marks and center marks in holes or on shafts and linear scores for scribing purposes in slot-like depressions are very time-consuming to carry out with precision and require manual skill, since it is difficult rapidly and precisely to determine the center of holes or the longitudinal center of slots and grooves; for this reason, errors frequently occur. It is also inconvenient to remove a broken screw from a workpiece. The broken screw present in the workpiece has to be drilled out, and it is generally only in exceptional cases that the center for positioning a drill bit for drilling out can be determined exactly. Where the operation is carried out imprecisely, the screw thread in the workpiece is damaged when the broken screw is drilled out, any repaired screw connection becomes insecure, and the new screw does not fit. The only remaining remedy is to cut a new thread in the workpiece and to use an appropriate screw. Rapid centering, for example on a screw, likewise dispenses with the inconvenient procedure of clamping in the lathe.